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C₂×#30058 #6434128

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4,8,12,9,13,22,7)(5,14,16,26,18,25,17,10)(6,19,20,28,21,29,23,11)(15,27,31,30,33,24,32,34);(3,5)(4,10)(6,15)(7,14)(8,17)(9,18)(11,27)(12,25)(13,26)(16,22)(19,34)(20,32)(21,33)(23,31)(24,28)(29,30);(3,6,9,21)(4,11,13,28)(5,15,18,33)(7,19,12,29)(8,23,22,20)(10,24,26,27)(14,30,25,34)(16,32,17,31);(3,7,22,13,9,12,8,4)(5,14,16,26,18,25,17,10)(6,11,23,29,21,28,20,19)(15,27,31,30,33,24,32,34)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6341324);